Answer
The last zero must be real otherwise the polynomial function will have a degree of $5$.
One of the missing zeros is $4+i$.
Work Step by Step
The Conjugate Pairs Theorem says that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. That is, if $a + bi$ is a zero then so is $a – bi$ and vice-versa.
We have that $-3$ and $(4-i)$ are zeros of $f(x)$, hence according to the Conjugate Pair Theorem $\overline{4-i}=4+i$ is also a zero of $f(x)$, hence $f(x)$ has at least 3 zeros, so in order for it to have 4 zeros, the fourth zero has to be a real (non-complex number), because if it was a complex number its conjugate pair would also be a zero, making the degree at least 5 according to the Conjugate Pair Theorem.